Abstract
In this paper we discuss the role of labels in transition systems with regard to bisimilarity and model checking problems. We suggest a general reduction from labelled transition systems to unlabelled ones, preserving bisimilarity and satisfiability of μ-calculus formulas. We apply the reduction to the class of transition systems generated by Petri nets and pushdown automata, and obtain several decidability/complexity corollaries for unlabelled systems. Probably the most interesting result is undecidability of strong bisimilarity for unlabelled Petri nets.
The author is supported in part by the GACR, grant No. 201/00/0400.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Ben-Ari, Z. Manna, and A. Pnueli. The temporal logic of branching time. Acta Informatica, 20(3):207–226, 1983.
O. Burkart and J. Esparza. More infinite results. Bulletin of the European Association for Theoretical Computer Science, 62:138–159, June 1997. Columns: Concurrency.
E.M. Clarke and E.A. Emerson. Design and synthesis of synchronization skeletons using branching time temporal logic. In Logic of Programs Workshop, volume 131 of LNCS, pages 52–71. Springer-Verlag, 1981.
E.M. Clarke, E.A. Emerson, and A.P. Sistla. Automatic verification of finite state concurrent systems using temporal logic specifications: A practical approach. ACM Transactions on Programming Languages and Systems, 8(2):244–263, 1986.
J. Esparza and A. Kiehn. On the model checking problem for branching time logics and basic parallel processes. In International Conference on Computer-Aided Verification (CAV’95), volume 939 of LNCS, pages 353–366, 1995.
J. Esparza. Decidability of model-checking for infinite-state concurrent systems. Acta Informatica, 34:85–107, 1997.
M. Hennessy and R. Milner. Algebraic laws for nondeterminism and concurrency. Journal of the Association for Computing Machinery, 32(1):137–161, 1985.
P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281–301, 1995.
P. Jancar, A. Kucera, and R. Mayr. Deciding bisimulation-like equivalences with finite-state processes. In Proceedings of the Annual International Colloquium on Automata, Languages and Programming (ICALP’98), volume 1443 of LNCS. Springer-Verlag, 1998.
P. Jancar and F. Moller. Checking regular properties of Petri nets. In Proceedings of CONCUR’95, volume 962 of LNCS, pages 348–362. Springer-Verlag, 1995.
R. Mayr. Strict lower bounds for model checking BPA. In Proceedings of the MFCS’98 Workshop on Concurrency, volume 18 of ENTCS. Springer-Verlag, 1998.
R. Mayr. On the complexity of bisimulation problems for pushdown automata. In IFIP International Conference on Theoretical Computer Science (IFIP TCS’2000), volume 1872 of LNCS. Springer-Verlag, 2000.
F. Moller. Infinite results. In Proceedings of CONCUR’96, volume 1119 of LNCS, pages 195–216. Springer-Verlag, 1996.
J.L. Peterson. Petri Net Theory and the Modelling of Systems. Prentice-Hall, 1981.
G. S’enizergues. Decidability of bisimulation equivalence for equational graphs of finite out-degree. In Proceedings of the 39th Annual Symposium on Foundations of Computer Science(FOCS-98), pages 120–129. IEEE Computer Society, 1998.
J. Srba. On the power of labels in transition systems. Technical Report RS-01-19, BRICS Research Series, 2001.
C. Stirling. Local model checking games. In Proceedings of the 6th International Conference on Concurrency Theory (CONCUR’95), volume 962 of LNCS, pages 1–11. Springer-Verlag, 1995.
W. Thomas. On the Ehrenfeucht-Fraïssé game in theoretical computer science (extended abstract). In Proceedings of the 4th International Joint Conference CAAP/FASE, Theory and Practice of Software Development (TAPSOFT’93), volume 668 of LNCS, pages 559–568. Springer-Verlag, 1993.
W. Vogler. Modular construction and partial order semantics of Petri nets, volume 625 of LNCS. Springer-Verlag, 1992.
I. Walukiewicz. Pushdown processes: Games and model checking. In International Conference on Computer-Aided Verification (CAV’96), volume 1102 of LNCS, pages 62–74, 1996. To appear in Information and Computation.
I. Walukiewicz. Model checking CTL properties of pushdown systems. In Proceedings Foundations of Software Technology and Theoretical Computer Science (FSTTCS’00), volume 1974 of LNCS, pages 127–138. Springer-Verlag, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Srba, J. (2001). On the Power of Labels in Transition Systems. In: Larsen, K.G., Nielsen, M. (eds) CONCUR 2001 — Concurrency Theory. CONCUR 2001. Lecture Notes in Computer Science, vol 2154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44685-0_19
Download citation
DOI: https://doi.org/10.1007/3-540-44685-0_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42497-0
Online ISBN: 978-3-540-44685-9
eBook Packages: Springer Book Archive